The question about the origin of planets and life has fascinated humanity since ancient times. In the last two decades thousands of exoplanets, i.e. planets around stars other than our Sun, have been discovered, challenging our understanding of how planets form. It is believed that planets form in disks around young stars. Recent observations suggest that planets and planetary systems may form much faster than it has been previously thought. I will present radiative hydrodynamic computational models of the process of planet formation in young protostellar disks, and I will discuss whether gravitational instability may be responsible for the fast formation of planets. I will also discuss how young planets evolve after they form and I will argue that their fate is quite diverse and depends on the detailed physics of their interaction with their parent disks.
